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Two approximations of solutions of Hamilton-Jacobi equations

Authors: M. G. Crandall and P.-L. Lions
Journal: Math. Comp. 43 (1984), 1-19
MSC: Primary 65M10; Secondary 35F20, 49C10
MathSciNet review: 744921
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Abstract: Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations, control theory and differential games. The associated initial-value problems almost never have global-time classical solutions, and one must deal with suitable generalized solutions. The correct class of generalized solutions has only recently been established by the authors. This article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates. Analogous results are proved by similar means for the method of vanishing viscosity.

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Keywords: Hamilton-Jacobi equations, difference approximations, error estimates, method of vanishing viscosity
Article copyright: © Copyright 1984 American Mathematical Society